MILAN, June 25 (Reuters) - Italy's Economy Minister Pier Carlo Padoan said on Saturday that Britain's vote to leave the European Union could lead to the Italian economy growing less than initially forecast, with a negative impact on public finances.

Italy, the euro zone's third largest economy, has posted weak growth since it emerged from a three-year recession at the start of 2015 and continues to lag the rest of the currency bloc.

"We have to be very clear: it can't be ruled out that, following Brexit, for reasons outside our control, the economic picture worsens and we will have less growth," Padoan told the Corriere della Sera daily in an interview.

"This will hit public finances. I hope it doesn't happen but it is probable."

The government's present forecast is for growth of 1.2 percent this year. Italy's public debt, at around 133 percent of gross domestic product, is the highest in the euro zone after Greece's.

Unicredit, the country's largest bank, said that following the British referendum it was slashing its 2017 growth forecast for Italy to between 0.2 and 0.7 percent, down from a previous 1.2 percent.

On Friday, the Italian economy ministry said Britain's decision could have a "limited" impact on growth.

Padoan told Corriere della Sera that to avoid the previously "unthinkable" risk that the British vote leads to other countries also leaving, the EU must now review its priorities.

"Europe can no longer only worry about banks," he said, calling for "common policies that don't only regard banking union but also immigration, security and the fight against inequality."

Ministers are making clear that they see the outcome of the British referendum offering opportunities for Italy as well as risks.

Industry Minister Carlo Calenda said Italy, which was granted what the European Commission called "unprecedented" budget flexibility for this year, would now call for the EU to make fiscal rules even more flexible as it prepares its 2017 budget.

He told financial daily Il Sole 24 Ore there was a need for "much more freedom of action" to allow countries to invest more in "culture, innovation and education," without falling foul of deficit limits.

Foreign Minister Paolo Gentiloni told Il Messaggero daily that Italy's role in Europe would increase because "before there were four principle players, now there are three."

Interior Minister Angelino Alfano said on Friday he believed Milan would become a more important financial hub as business moves away from London. (reporting by Giulia Segreti and Gavin Jones; Editing by Toby Chopra)